integral

Let B be a ring with a subring A. We will assume that A is contained in the center of B (in particular, A is commutative). An element x∈B is integral over A if there exist elements a0,…,an-1∈A such that

xn+an-1⁢xn-1+⋯+a1⁢x+a0=0.

The ring B is integral over A if every element of B is integral over A.